 # Entropy, Free Energy, and Equilibrium

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Entropy, Free Energy, and Equilibrium
Chapter 17 Copyright © The McGraw-Hill Companies, Inc.  Permission required for reproduction or display.

Spontaneous Physical and Chemical Processes
A waterfall runs downhill A lump of sugar dissolves in a cup of coffee At 1 atm, water freezes below 0 oC and ice melts above 0 oC Heat flows from a hotter object to a colder object A gas expands in an evacuated bulb Iron exposed to oxygen and water forms rust spontaneous nonspontaneous

spontaneous nonspontaneous

Does a decrease in enthalpy mean a reaction proceeds spontaneously?
Spontaneous reactions CH4 (g) + 2O2 (g) CO2 (g) + 2H2O (l) DH0 = kJ/mol H+ (aq) + OH- (aq) H2O (l) DH0 = kJ/mol H2O (s) H2O (l) DH0 = 6.01 kJ/mol NH4NO3 (s) NH4+(aq) + NO3- (aq) DH0 = 25 kJ/mol H2O

Entropy (S) is a measure of the randomness or disorder of a system.
DS = Sf - Si If the change from initial to final results in an increase in randomness Sf > Si DS > 0 For any substance, the solid state is more ordered than the liquid state and the liquid state is more ordered than gas state. Ssolid < Sliquid << Sgas H2O (s) H2O (l) DS > 0

Entropy W = number of microstates S = k ln W DS = Sf - Si DS = k ln Wf Wi Wf > Wi then DS > 0 Wf < Wi then DS < 0

Processes that lead to an increase in entropy (DS > 0)

Example: Br2(l) Br2(g) Example: I2(s) I2(g) DS > 0 DS > 0

Entropy State functions are properties that are determined by the state of the system, regardless of how that condition was achieved. Examples: energy, enthalpy, pressure, volume, temperature , entropy Review Potential energy of hiker 1 and hiker 2 is the same even though they took different paths.

17.1 Predict whether the entropy change is greater or less than zero for each of the following processes: (a) freezing ethanol (b) evaporating a beaker of liquid bromine at room temperature (c) dissolving glucose in water (d) cooling nitrogen gas from 80°C to 20°C

First Law of Thermodynamics
Energy can be converted from one form to another but energy cannot be created or destroyed. Second Law of Thermodynamics The entropy of the universe increases in a spontaneous process and remains unchanged in an equilibrium process. Spontaneous process: DSuniv = DSsys + DSsurr > 0 Equilibrium process: DSuniv = DSsys + DSsurr = 0

Entropy Changes in the System (DSsys)
The standard entropy of reaction (DS0 ) is the entropy change for a reaction carried out at 1 atm and 250C. rxn aA + bB cC + dD DS0 rxn dS0(D) cS0(C) = [ + ] - bS0(B) aS0(A) DS0 rxn nS0(products) = S mS0(reactants) -

17.2 From the standard entropy values in Appendix 3, calculate the standard entropy changes for the following reactions at 25°C. CaCO3(s) CaO(s) + CO2(g) (b) N2(g) + 3H2(g) NH3(g) (c) H2(g) + Cl2(g) HCl(g)

Entropy Changes in the System (DSsys)
When gases are produced (or consumed) If a reaction produces more gas molecules than it consumes, DS0 > 0. If the total number of gas molecules diminishes, DS0 < 0. If there is no net change in the total number of gas molecules, then DS0 may be positive or negative BUT DS0 will be a small number.

17.3 Predict whether the entropy change of the system in each of the following reactions is positive or negative. 2H2(g) + O2(g) 2H2O(l) (b) NH4Cl(s) NH3(g) + HCl(g) (c) H2(g) + Br2(g) 2HBr(g)

Entropy Changes in the Surroundings (DSsurr)
Exothermic Process DSsurr > 0 Endothermic Process DSsurr < 0

Third Law of Thermodynamics
The entropy of a perfect crystalline substance is zero at the absolute zero of temperature. S = k ln W W = 1 S = 0

For a constant temperature and constant pressure process:
Gibbs Free Energy Spontaneous process: DSuniv = DSsys + DSsurr > 0 Equilibrium process: DSuniv = DSsys + DSsurr = 0 For a constant temperature and constant pressure process: Gibbs free energy (G) DG = DHsys -TDSsys DG < The reaction is spontaneous in the forward direction. DG > The reaction is nonspontaneous as written. The reaction is spontaneous in the reverse direction. DG = The reaction is at equilibrium.

DG0 of any element in its stable form is zero.
The standard free-energy of reaction (DG0 ) is the free-energy change for a reaction when it occurs under standard-state conditions. rxn aA + bB cC + dD DG0 rxn dDG0 (D) f cDG0 (C) = [ + ] - bDG0 (B) aDG0 (A) DG0 rxn nDG0 (products) f = S mDG0 (reactants) - Standard free energy of formation (DG0) is the free-energy change that occurs when 1 mole of the compound is formed from its elements in their standard states. f DG0 of any element in its stable form is zero. f

17.4 Calculate the standard free-energy changes for the following reactions at 25°C. CH4(g) + 2O2(g) CO2(g) + 2H2O(l) (b) 2MgO(s) 2Mg(s) + O2(g)

DG = DH - TDS

Equilibrium Pressure of CO2
Temperature and Spontaneity of Chemical Reactions CaCO3 (s) CaO (s) + CO2 (g) Equilibrium Pressure of CO2 DH0 = kJ/mol DS0 = J/K·mol DG0 = DH0 – TDS0 At 25 oC, DG0 = kJ/mol DG0 = 0 at 835 oC

Gibbs Free Energy and Phase Transitions
DG0 = 0 = DH0 – TDS0 H2O (l) H2O (g) DS = T DH = 40.79 kJ/mol 373 K = 1.09 x 10-1 kJ/K·mol = 109 J/K·mol

17.5 The molar heats of fusion and vaporization of benzene are
10.9 kJ/mol and 31.0 kJ/mol, respectively. Calculate the entropy changes for the solid → liquid and liquid → vapor transitions for benzene. At 1 atm pressure, benzene melts at 5.5°C and boils at 80.1°C.

Gibbs Free Energy and Chemical Equilibrium
DG = DG0 + RT lnQ R is the gas constant (8.314 J/K•mol) T is the absolute temperature (K) Q is the reaction quotient At Equilibrium DG = 0 Q = K 0 = DG0 + RT lnK DG0 = - RT lnK

Free Energy Versus Extent of Reaction
DG0 > 0 DG0 < 0

DG0 = - RT lnK

17.6 Using data listed in Appendix 3, calculate the equilibrium constant (KP) for the following reaction at 25°C: 2H2O(l) H2(g) + O2(g)

AgCl(s) Ag+(aq) + Cl-(aq)
17.7 In Chapter 16 we discussed the solubility product of slightly soluble substances. Using the solubility product of silver chloride at 25°C (1.6 x 10-10), calculate ΔG° for the process AgCl(s) Ag+(aq) + Cl-(aq)

17.8 The equilibrium constant (KP) for the reaction N2O4(g) 2NO2(g)
is at 298 K, which corresponds to a standard free-energy change of 5.40 kJ/mol. In a certain experiment, the initial pressures are PNO2 = atm and PN2O4 = atm. Calculate ΔG for the reaction at these pressures and predict the direction of the net reaction toward equilibrium.